Set Operations

1. With any two sets “A” and “B” there is associated a third set “C” satisfying the property that C = { X/X Є AV x Є B }

In words: “C” is equal to X, such that X is belong to “A” or X is an element of B

“C” is called the union of “A” and “B” we denote the set C symbolically as C = A U B

Example:
A = {3, 4, 5, 6, 7}
B = {2, 4, 6, 8, 10}
A U B = {2, 3, 4, 5, 6, 7, 8, 10}

2. With any two sets A & B there is associated A third set “D” satisfying the property that D = { X/X Є A ۸ X Є B}

In words: D equals X such that X is an element of set “A” and x is a member of B.

“D” is called the intersection of sets A and B, and we denote the set D symbolically as D = A B

3. With any two sets A and B there is associated A third set “C” satisfying the property that C = { X/X Є A ۸ X € B}. We denote the set symbolically as C = A – B, and call C the relative complement or difference of A and B.

Example:
A = { a, b, c, d, e, f}
B = { a, e, i, o, u}
A – B = {b, c, d, f} and B – A = {i, o, u}

4. If A is a subset of U, then the set of an elements contained in U that are not elements of A is called the complement of A in U and is designated by Ă then Ă = {X/X Є U ۸ X € A}

Example: Consider the universal set of an counting nos. and the set A of counting numbers less than 100 then

U = {1, 2, 3, 4, ……} A = { 1, 2, 3,……99}

Ă = {100, 101, 103…….}

5. The set product or cartesian product of two sets A and B is the set of an possible ordered pairs (a, b) where a is in A and b is in B. We symbolize this set of ordered pairs by A X B and write,
A X B = {(a,b) / a Є A ۸ b Є B }

Example:

If A = {1, 2} and B = {x, y} then A X B = { (1, x), (1, y), (2, x) , (2, y}} and B X A = {(X, 1), (X, 2), (Y, 1), (Y, 2)}